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      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "from torch.distributions import multinomial\n",
    "from d2l import torch as d2l\n",
    "\n",
    "fair_probs = torch.ones([6]) / 6\n",
    "multinomial.Multinomial(1, fair_probs).sample()"
   ]
  },
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   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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      ]
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     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "counts = multinomial.Multinomial(10000, fair_probs).sample()\n",
    "counts / 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
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   "source": [
    "counts = multinomial.Multinomial(100, fair_probs).sample((500,))\n",
    "cum_counts = counts.cumsum(dim=0)\n",
    "estimates = cum_counts / cum_counts.sum(dim=1, keepdims=True)\n",
    "\n",
    "d2l.set_figsize((6, 4.5))\n",
    "for i in range(6):\n",
    "    d2l.plt.plot(estimates[:, i].numpy(), label=(\"P(die=\" + str(i + 1) + \")\"))\n",
    "d2l.plt.axhline(y=0.167, color='black', linestyle='dashed')\n",
    "d2l.plt.gca().set_xlabel('Groups of experiments')\n",
    "d2l.plt.gca().set_ylabel('Estimated probability')\n",
    "d2l.plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['AbsTransform', 'AffineTransform', 'Bernoulli', 'Beta', 'Binomial', 'CatTransform', 'Categorical', 'Cauchy', 'Chi2', 'ComposeTransform', 'ContinuousBernoulli', 'CorrCholeskyTransform', 'Dirichlet', 'Distribution', 'ExpTransform', 'Exponential', 'ExponentialFamily', 'FisherSnedecor', 'Gamma', 'Geometric', 'Gumbel', 'HalfCauchy', 'HalfNormal', 'Independent', 'IndependentTransform', 'Kumaraswamy', 'LKJCholesky', 'Laplace', 'LogNormal', 'LogisticNormal', 'LowRankMultivariateNormal', 'LowerCholeskyTransform', 'MixtureSameFamily', 'Multinomial', 'MultivariateNormal', 'NegativeBinomial', 'Normal', 'OneHotCategorical', 'OneHotCategoricalStraightThrough', 'Pareto', 'Poisson', 'PowerTransform', 'RelaxedBernoulli', 'RelaxedOneHotCategorical', 'ReshapeTransform', 'SigmoidTransform', 'SoftmaxTransform', 'StackTransform', 'StickBreakingTransform', 'StudentT', 'TanhTransform', 'Transform', 'TransformedDistribution', 'Uniform', 'VonMises', 'Weibull', '__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__path__', '__spec__', 'bernoulli', 'beta', 'biject_to', 'binomial', 'categorical', 'cauchy', 'chi2', 'constraint_registry', 'constraints', 'continuous_bernoulli', 'dirichlet', 'distribution', 'exp_family', 'exponential', 'fishersnedecor', 'gamma', 'geometric', 'gumbel', 'half_cauchy', 'half_normal', 'identity_transform', 'independent', 'kl', 'kl_divergence', 'kumaraswamy', 'laplace', 'lkj_cholesky', 'log_normal', 'logistic_normal', 'lowrank_multivariate_normal', 'mixture_same_family', 'multinomial', 'multivariate_normal', 'negative_binomial', 'normal', 'one_hot_categorical', 'pareto', 'poisson', 'register_kl', 'relaxed_bernoulli', 'relaxed_categorical', 'studentT', 'transform_to', 'transformed_distribution', 'transforms', 'uniform', 'utils', 'von_mises', 'weibull']\n"
     ]
    }
   ],
   "source": [
    "print(dir(torch.distributions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on built-in function ones:\n",
      "\n",
      "ones(...)\n",
      "    ones(*size, *, out=None, dtype=None, layout=torch.strided, device=None, requires_grad=False) -> Tensor\n",
      "    \n",
      "    Returns a tensor filled with the scalar value `1`, with the shape defined\n",
      "    by the variable argument :attr:`size`.\n",
      "    \n",
      "    Args:\n",
      "        size (int...): a sequence of integers defining the shape of the output tensor.\n",
      "            Can be a variable number of arguments or a collection like a list or tuple.\n",
      "    \n",
      "    Keyword arguments:\n",
      "        out (Tensor, optional): the output tensor.\n",
      "        dtype (:class:`torch.dtype`, optional): the desired data type of returned tensor.\n",
      "            Default: if ``None``, uses a global default (see :func:`torch.set_default_tensor_type`).\n",
      "        layout (:class:`torch.layout`, optional): the desired layout of returned Tensor.\n",
      "            Default: ``torch.strided``.\n",
      "        device (:class:`torch.device`, optional): the desired device of returned tensor.\n",
      "            Default: if ``None``, uses the current device for the default tensor type\n",
      "            (see :func:`torch.set_default_tensor_type`). :attr:`device` will be the CPU\n",
      "            for CPU tensor types and the current CUDA device for CUDA tensor types.\n",
      "        requires_grad (bool, optional): If autograd should record operations on the\n",
      "            returned tensor. Default: ``False``.\n",
      "    \n",
      "    Example::\n",
      "    \n",
      "        >>> torch.ones(2, 3)\n",
      "        tensor([[ 1.,  1.,  1.],\n",
      "                [ 1.,  1.,  1.]])\n",
      "    \n",
      "        >>> torch.ones(5)\n",
      "        tensor([ 1.,  1.,  1.,  1.,  1.])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(torch.ones)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.ones(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.ones??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数后加`？`和`help`效果相同，`？？`会显示出函数python代码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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